/*
 * @(#)Quantize.java    0.90 9/19/00 Adam Doppelt
 */

package com.panayotis.jubler.subs.color;

/**
 * An efficient color quantization algorithm, adapted from the C++
 * implementation quantize.c in <a
 * href="http://www.imagemagick.org/">ImageMagick</a>. The pixels for an image
 * are placed into an oct tree. The oct tree is reduced in size, and the pixels
 * from the original image are reassigned to the nodes in the reduced tree.<p>
 *
 * Here is the copyright notice from ImageMagick:
 *
 * <pre>
 * %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 * %  Permission is hereby granted, free of charge, to any person obtaining a    %
 * %  copy of this software and associated documentation files ("ImageMagick"),  %
 * %  to deal in ImageMagick without restriction, including without limitation   %
 * %  the rights to use, copy, modify, merge, publish, distribute, sublicense,   %
 * %  and/or sell copies of ImageMagick, and to permit persons to whom the       %
 * %  ImageMagick is furnished to do so, subject to the following conditions:    %
 * %                                                                             %
 * %  The above copyright notice and this permission notice shall be included in %
 * %  all copies or substantial portions of ImageMagick.                         %
 * %                                                                             %
 * %  The software is provided "as is", without warranty of any kind, express or %
 * %  implied, including but not limited to the warranties of merchantability,   %
 * %  fitness for a particular purpose and noninfringement.  In no event shall   %
 * %  E. I. du Pont de Nemours and Company be liable for any claim, damages or   %
 * %  other liability, whether in an action of contract, tort or otherwise,      %
 * %  arising from, out of or in connection with ImageMagick or the use or other %
 * %  dealings in ImageMagick.                                                   %
 * %                                                                             %
 * %  Except as contained in this notice, the name of the E. I. du Pont de       %
 * %  Nemours and Company shall not be used in advertising or otherwise to       %
 * %  promote the sale, use or other dealings in ImageMagick without prior       %
 * %  written authorization from the E. I. du Pont de Nemours and Company.       %
 * %                                                                             %
 * %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 * </pre>
 *
 *
 * @version 0.90 19 Sep 2000
 * @author <a href="http://www.gurge.com/amd/">Adam Doppelt</a>
 */
public class Quantize {

    /**
     * <pre>
     * %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     * %                                                                             %
     * %                                                                             %
     * %                                                                             %
     * %           QQQ   U   U   AAA   N   N  TTTTT  IIIII   ZZZZZ  EEEEE            %
     * %          Q   Q  U   U  A   A  NN  N    T      I        ZZ  E                %
     * %          Q   Q  U   U  AAAAA  N N N    T      I      ZZZ   EEEEE            %
     * %          Q  QQ  U   U  A   A  N  NN    T      I     ZZ     E                %
     * %           QQQQ   UUU   A   A  N   N    T    IIIII   ZZZZZ  EEEEE            %
     * %                                                                             %
     * %                                                                             %
     * %              Reduce the Number of Unique Colors in an Image                 %
     * %                                                                             %
     * %                                                                             %
     * %                           Software Design                                   %
     * %                             John Cristy                                     %
     * %                              July 1992                                      %
     * %                                                                             %
     * %                                                                             %
     * %  Copyright 1998 E. I. du Pont de Nemours and Company                        %
     * %                                                                             %
     * %  Permission is hereby granted, free of charge, to any person obtaining a    %
     * %  copy of this software and associated documentation files ("ImageMagick"),  %
     * %  to deal in ImageMagick without restriction, including without limitation   %
     * %  the rights to use, copy, modify, merge, publish, distribute, sublicense,   %
     * %  and/or sell copies of ImageMagick, and to permit persons to whom the       %
     * %  ImageMagick is furnished to do so, subject to the following conditions:    %
     * %                                                                             %
     * %  The above copyright notice and this permission notice shall be included in %
     * %  all copies or substantial portions of ImageMagick.                         %
     * %                                                                             %
     * %  The software is provided "as is", without warranty of any kind, express or %
     * %  implied, including but not limited to the warranties of merchantability,   %
     * %  fitness for a particular purpose and noninfringement.  In no event shall   %
     * %  E. I. du Pont de Nemours and Company be liable for any claim, damages or   %
     * %  other liability, whether in an action of contract, tort or otherwise,      %
     * %  arising from, out of or in connection with ImageMagick or the use or other %
     * %  dealings in ImageMagick.                                                   %
     * %                                                                             %
     * %  Except as contained in this notice, the name of the E. I. du Pont de       %
     * %  Nemours and Company shall not be used in advertising or otherwise to       %
     * %  promote the sale, use or other dealings in ImageMagick without prior       %
     * %  written authorization from the E. I. du Pont de Nemours and Company.       %
     * %                                                                             %
     * %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     * %
     * %  Realism in computer graphics typically requires using 24 bits/pixel to
     * %  generate an image. Yet many graphic display devices do not contain
     * %  the amount of memory necessary to match the spatial and color
     * %  resolution of the human eye. The QUANTIZE program takes a 24 bit
     * %  image and reduces the number of colors so it can be displayed on
     * %  raster device with less bits per pixel. In most instances, the
     * %  quantized image closely resembles the original reference image.
     * %
     * %  A reduction of colors in an image is also desirable for image
     * %  transmission and real-time animation.
     * %
     * %  Function Quantize takes a standard RGB or monochrome images and quantizes
     * %  them down to some fixed number of colors.
     * %
     * %  For purposes of color allocation, an image is a set of n pixels, where
     * %  each pixel is a point in RGB space. RGB space is a 3-dimensional
     * %  vector space, and each pixel, pi, is defined by an ordered triple of
     * %  red, green, and blue coordinates, (ri, gi, bi).
     * %
     * %  Each primary color component (red, green, or blue) represents an
     * %  intensity which varies linearly from 0 to a maximum value, cmax, which
     * %  corresponds to full saturation of that color. Color allocation is
     * %  defined over a domain consisting of the cube in RGB space with
     * %  opposite vertices at (0,0,0) and (cmax,cmax,cmax). QUANTIZE requires
     * %  cmax = 255.
     * %
     * %  The algorithm maps this domain onto a tree in which each node
     * %  represents a cube within that domain. In the following discussion
     * %  these cubes are defined by the coordinate of two opposite vertices:
     * %  The vertex nearest the origin in RGB space and the vertex farthest
     * %  from the origin.
     * %
     * %  The tree's root node represents the the entire domain, (0,0,0) through
     * %  (cmax,cmax,cmax). Each lower level in the tree is generated by
     * %  subdividing one node's cube into eight smaller cubes of equal size.
     * %  This corresponds to bisecting the parent cube with planes passing
     * %  through the midpoints of each edge.
     * %
     * %  The basic algorithm operates in three phases: Classification,
     * %  Reduction, and Assignment. Classification builds a color
     * %  description tree for the image. Reduction collapses the tree until
     * %  the number it represents, at most, the number of colors desired in the
     * %  output image. Assignment defines the output image's color map and
     * %  sets each pixel's color by reclassification in the reduced tree.
     * %  Our goal is to minimize the numerical discrepancies between the original
     * %  colors and quantized colors (quantization error).
     * %
     * %  Classification begins by initializing a color description tree of
     * %  sufficient depth to represent each possible input color in a leaf.
     * %  However, it is impractical to generate a fully-formed color
     * %  description tree in the classification phase for realistic values of
     * %  cmax. If colors components in the input image are quantized to k-bit
     * %  precision, so that cmax= 2k-1, the tree would need k levels below the
     * %  root node to allow representing each possible input color in a leaf.
     * %  This becomes prohibitive because the tree's total number of nodes is
     * %  1 + sum(i=1,k,8k).
     * %
     * %  A complete tree would require 19,173,961 nodes for k = 8, cmax = 255.
     * %  Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
     * %  Initializes data structures for nodes only as they are needed;  (2)
     * %  Chooses a maximum depth for the tree as a function of the desired
     * %  number of colors in the output image (currently log2(colormap size)).
     * %
     * %  For each pixel in the input image, classification scans downward from
     * %  the root of the color description tree. At each level of the tree it
     * %  identifies the single node which represents a cube in RGB space
     * %  containing the pixel's color. It updates the following data for each
     * %  such node:
     * %
     * %    n1: Number of pixels whose color is contained in the RGB cube
     * %    which this node represents;
     * %
     * %    n2: Number of pixels whose color is not represented in a node at
     * %    lower depth in the tree;  initially,  n2 = 0 for all nodes except
     * %    leaves of the tree.
     * %
     * %    Sr, Sg, Sb: Sums of the red, green, and blue component values for
     * %    all pixels not classified at a lower depth. The combination of
     * %    these sums and n2  will ultimately characterize the mean color of a
     * %    set of pixels represented by this node.
     * %
     * %    E: The distance squared in RGB space between each pixel contained
     * %    within a node and the nodes' center. This represents the quantization
     * %    error for a node.
     * %
     * %  Reduction repeatedly prunes the tree until the number of nodes with
     * %  n2 > 0 is less than or equal to the maximum number of colors allowed
     * %  in the output image. On any given iteration over the tree, it selects
     * %  those nodes whose E count is minimal for pruning and merges their
     * %  color statistics upward. It uses a pruning threshold, Ep, to govern
     * %  node selection as follows:
     * %
     * %    Ep = 0
     * %    while number of nodes with (n2 > 0) > required maximum number of colors
     * %      prune all nodes such that E &lt= Ep
     * %      Set Ep to minimum E in remaining nodes
     * %
     * %  This has the effect of minimizing any quantization error when merging
     * %  two nodes together.
     * %
     * %  When a node to be pruned has offspring, the pruning procedure invokes
     * %  itself recursively in order to prune the tree from the leaves upward.
     * %  n2,  Sr, Sg,  and  Sb in a node being pruned are always added to the
     * %  corresponding data in that node's parent. This retains the pruned
     * %  node's color characteristics for later averaging.
     * %
     * %  For each node, n2 pixels exist for which that node represents the
     * %  smallest volume in RGB space containing those pixel's colors. When n2
     * %  > 0 the node will uniquely define a color in the output image. At the
     * %  beginning of reduction,  n2 = 0  for all nodes except a the leaves of
     * %  the tree which represent colors present in the input image.
     * %
     * %  The other pixel count, n1, indicates the total number of colors
     * %  within the cubic volume which the node represents. This includes n1 -
     * %  n2  pixels whose colors should be defined by nodes at a lower level in
     * %  the tree.
     * %
     * %  Assignment generates the output image from the pruned tree. The
     * %  output image consists of two parts: (1)  A color map, which is an
     * %  array of color descriptions (RGB triples) for each color present in
     * %  the output image;  (2)  A pixel array, which represents each pixel as
     * %  an index into the color map array.
     * %
     * %  First, the assignment phase makes one pass over the pruned color
     * %  description tree to establish the image's color map. For each node
     * %  with n2  > 0, it divides Sr, Sg, and Sb by n2 . This produces the
     * %  mean color of all pixels that classify no lower than this node. Each
     * %  of these colors becomes an entry in the color map.
     * %
     * %  Finally,  the assignment phase reclassifies each pixel in the pruned
     * %  tree to identify the deepest node containing the pixel's color. The
     * %  pixel's value in the pixel array becomes the index of this node's mean
     * %  color in the color map.
     * %
     * %  With the permission of USC Information Sciences Institute, 4676 Admiralty
     * %  Way, Marina del Rey, California  90292, this code was adapted from module
     * %  ALCOLS written by Paul Raveling.
     * %
     * %  The names of ISI and USC are not used in advertising or publicity
     * %  pertaining to distribution of the software without prior specific
     * %  written permission from ISI.
     * % </pre>
     */
    final static boolean QUICK = true;
    final static int MAX_RGB = 255;
    final static int MAX_NODES = 266817;
    final static int MAX_TREE_DEPTH = 8;
    // these are precomputed in advance
    static int SQUARES[];
    static int SHIFT[];

    static {
        SQUARES = new int[MAX_RGB + MAX_RGB + 1];
        for (int i = -MAX_RGB; i <= MAX_RGB; i++)
            SQUARES[i + MAX_RGB] = i * i;

        SHIFT = new int[MAX_TREE_DEPTH + 1];
        for (int i = 0; i < MAX_TREE_DEPTH + 1; ++i)
            SHIFT[i] = 1 << (15 - i);
    }

    /**
     * Reduce the image to the given number of colors. The pixels are reduced in
     * place.
     *
     * @return The new color palette.
     */
    public static int[] quantizeImage(int pixels[][], int max_colors) {
        Cube cube = new Cube(pixels, max_colors);
        cube.classification();
        cube.reduction();
        cube.assignment();
        return cube.colormap;
    }

    static class Cube {

        int pixels[][];
        int max_colors;
        int colormap[];
        Node root;
        int depth;
        // counter for the number of colors in the cube. this gets
        // recalculated often.
        int colors;
        // counter for the number of nodes in the tree
        int nodes;

        Cube(int pixels[][], int max_colors) {
            this.pixels = pixels;
            this.max_colors = max_colors;

            int i = max_colors;
            // tree_depth = log max_colors
            //                 4
            for (depth = 1; i != 0; depth++)
                i /= 4;
            if (depth > 1)
                --depth;
            if (depth > MAX_TREE_DEPTH)
                depth = MAX_TREE_DEPTH;
            else if (depth < 2)
                depth = 2;

            root = new Node(this);
        }

        /**
         * Procedure Classification begins by initializing a color description
         * tree of sufficient depth to represent each possible input color in a
         * leaf. However, it is impractical to generate a fully-formed color
         * description tree in the classification phase for realistic values of
         * cmax. If colors components in the input image are quantized to k-bit
         * precision, so that cmax= 2k-1, the tree would need k levels below the
         * root node to allow representing each possible input color in a leaf.
         * This becomes prohibitive because the tree's total number of nodes is
         * 1 + sum(i=1,k,8k).<br><br>
         *
         * A complete tree would require 19,173,961 nodes for k = 8, cmax = 255.
         * Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
         * Initializes data structures for nodes only as they are needed; (2)
         * Chooses a maximum depth for the tree as a function of the desired
         * number of colors in the output image (currently log2(colormap
         * size)).<br><br>
         *
         * For each pixel in the input image, classification scans downward from
         * the root of the color description tree. At each level of the tree it
         * identifies the single node which represents a cube in RGB space
         * containing It updates the following data for each such node:
         * <ol>
         * <li>number_pixels : Number of pixels whose color is contained in the
         * RGB cube which this node represents;</li>
         *
         * <li>unique : Number of pixels whose color is not represented in a
         * node at lower depth in the tree; initially, n2 = 0 for all nodes
         * except leaves of the tree.</li>
         *
         * <li>total_red/green/blue : Sums of the red, green, and blue component
         * values for all pixels not classified at a lower depth. The
         * combination of these sums and n2 will ultimately characterize the
         * mean color of a set of pixels represented by this node.</li>
         * </ol>
         */
        void classification() {
            int pixels[][] = this.pixels;

            int width = pixels.length;
            int height = pixels[0].length;

            // convert to indexed color
            for (int x = width; x-- > 0;)
                for (int y = height; y-- > 0;) {
                    int pixel = pixels[x][y];
                    int red = (pixel >> 16) & 0xFF;
                    int green = (pixel >> 8) & 0xFF;
                    int blue = (pixel >> 0) & 0xFF;

                    // a hard limit on the number of nodes in the tree
                    if (nodes > MAX_NODES) {
                        System.out.println("pruning");
                        root.pruneLevel();
                        --depth;
                    }

                    // walk the tree to depth, increasing the
                    // number_pixels count for each node
                    Node node = root;
                    for (int level = 1; level <= depth; ++level) {
                        int id = (((red > node.mid_red ? 1 : 0) << 0)
                                | ((green > node.mid_green ? 1 : 0) << 1)
                                | ((blue > node.mid_blue ? 1 : 0) << 2));
                        if (node.child[id] == null)
                            new Node(node, id, level);
                        node = node.child[id];
                        node.number_pixels += SHIFT[level];
                    }

                    ++node.unique;
                    node.total_red += red;
                    node.total_green += green;
                    node.total_blue += blue;
                }
        }

        /**
         * reduction repeatedly prunes the tree until the number of nodes with
         * unique > 0 is less than or equal to the maximum number of colors
         * allowed in the output image.
         *
         * When a node to be pruned has offspring, the pruning procedure invokes
         * itself recursively in order to prune the tree from the leaves upward.
         * The statistics of the node being pruned are always added to the
         * corresponding data in that node's parent. This retains the pruned
         * node's color characteristics for later averaging.
         */
        void reduction() {
            int threshold = 1;
            while (colors > max_colors) {
                colors = 0;
                threshold = root.reduce(threshold, Integer.MAX_VALUE);
            }
        }

        /**
         * The result of a closest color search.
         */
        static class Search {

            int distance;
            int color_number;
        }

        /**
         * Procedure assignment generates the output image from the pruned tree.
         * The output image consists of two parts: (1) A color map, which is an
         * array of color descriptions (RGB triples) for each color present in
         * the output image; (2) A pixel array, which represents each pixel as
         * an index into the color map array.<br><br>
         *
         * First, the assignment phase makes one pass over the pruned color
         * description tree to establish the image's color map. For each node
         * with n2 > 0, it divides Sr, Sg, and Sb by n2. This produces the mean
         * color of all pixels that classify no lower than this node. Each of
         * these colors becomes an entry in the color map.<br><br>
         *
         * Finally, the assignment phase reclassifies each pixel in the pruned
         * tree to identify the deepest node containing the pixel's color. The
         * pixel's value in the pixel array becomes the index of this node's
         * mean color in the color map.
         */
        void assignment() {
            colormap = new int[colors];

            colors = 0;
            root.colormap();

            int pixels[][] = this.pixels;

            int width = pixels.length;
            int height = pixels[0].length;

            Search search = new Search();

            // convert to indexed color
            for (int x = width; x-- > 0;)
                for (int y = height; y-- > 0;) {
                    int pixel = pixels[x][y];
                    int red = (pixel >> 16) & 0xFF;
                    int green = (pixel >> 8) & 0xFF;
                    int blue = (pixel >> 0) & 0xFF;

                    // walk the tree to find the cube containing that color
                    Node node = root;
                    for (;;) {
                        int id = (((red > node.mid_red ? 1 : 0) << 0)
                                | ((green > node.mid_green ? 1 : 0) << 1)
                                | ((blue > node.mid_blue ? 1 : 0) << 2));
                        if (node.child[id] == null)
                            break;
                        node = node.child[id];
                    }

                    if (QUICK)
                        // if QUICK is set, just use that
                        // node. Strictly speaking, this isn't
                        // necessarily best match.
                        pixels[x][y] = node.color_number;
                    else {
                        // Find the closest color.
                        search.distance = Integer.MAX_VALUE;
                        node.parent.closestColor(red, green, blue, search);
                        pixels[x][y] = search.color_number;
                    }
                }
        }

        /**
         * A single Node in the tree.
         */
        static class Node {

            Cube cube;
            // parent node
            Node parent;
            // child nodes
            Node child[];
            int nchild;
            // our index within our parent
            int id;
            // our level within the tree
            int level;
            // our color midpoint
            int mid_red;
            int mid_green;
            int mid_blue;
            // the pixel count for this node and all children
            int number_pixels;
            // the pixel count for this node
            int unique;
            // the sum of all pixels contained in this node
            int total_red;
            int total_green;
            int total_blue;
            // used to build the colormap
            int color_number;

            Node(Cube cube) {
                this.cube = cube;
                this.parent = this;
                this.child = new Node[8];
                this.id = 0;
                this.level = 0;

                this.number_pixels = Integer.MAX_VALUE;

                this.mid_red = (MAX_RGB + 1) >> 1;
                this.mid_green = (MAX_RGB + 1) >> 1;
                this.mid_blue = (MAX_RGB + 1) >> 1;
            }

            Node(Node parent, int id, int level) {
                this.cube = parent.cube;
                this.parent = parent;
                this.child = new Node[8];
                this.id = id;
                this.level = level;

                // add to the cube
                ++cube.nodes;
                if (level == cube.depth)
                    ++cube.colors;

                // add to the parent
                ++parent.nchild;
                parent.child[id] = this;

                // figure out our midpoint
                int bi = (1 << (MAX_TREE_DEPTH - level)) >> 1;
                mid_red = parent.mid_red + ((id & 1) > 0 ? bi : -bi);
                mid_green = parent.mid_green + ((id & 2) > 0 ? bi : -bi);
                mid_blue = parent.mid_blue + ((id & 4) > 0 ? bi : -bi);
            }

            /**
             * Remove this child node, and make sure our parent absorbs our
             * pixel statistics.
             */
            void pruneChild() {
                --parent.nchild;
                parent.unique += unique;
                parent.total_red += total_red;
                parent.total_green += total_green;
                parent.total_blue += total_blue;
                parent.child[id] = null;
                --cube.nodes;
                cube = null;
                parent = null;
            }

            /**
             * Prune the lowest layer of the tree.
             */
            void pruneLevel() {
                if (nchild != 0)
                    for (int id = 0; id < 8; id++)
                        if (child[id] != null)
                            child[id].pruneLevel();
                if (level == cube.depth)
                    pruneChild();
            }

            /**
             * Remove any nodes that have fewer than threshold pixels. Also, as
             * long as we're walking the tree:
             *
             * - figure out the color with the fewest pixels - recalculate the
             * total number of colors in the tree
             */
            int reduce(int threshold, int next_threshold) {
                if (nchild != 0)
                    for (int id = 0; id < 8; id++)
                        if (child[id] != null)
                            next_threshold = child[id].reduce(threshold, next_threshold);
                if (number_pixels <= threshold)
                    pruneChild();
                else {
                    if (unique != 0)
                        cube.colors++;
                    if (number_pixels < next_threshold)
                        next_threshold = number_pixels;
                }
                return next_threshold;
            }

            /**
             * colormap traverses the color cube tree and notes each colormap
             * entry. A colormap entry is any node in the color cube tree where
             * the number of unique colors is not zero.
             */
            void colormap() {
                if (nchild != 0)
                    for (int id = 0; id < 8; id++)
                        if (child[id] != null)
                            child[id].colormap();
                if (unique != 0) {
                    int r = ((total_red + (unique >> 1)) / unique);
                    int g = ((total_green + (unique >> 1)) / unique);
                    int b = ((total_blue + (unique >> 1)) / unique);
                    cube.colormap[cube.colors] = (((0xFF) << 24)
                            | ((r & 0xFF) << 16)
                            | ((g & 0xFF) << 8)
                            | ((b & 0xFF) << 0));
                    color_number = cube.colors++;
                }
            }

            /**
             * ClosestColor traverses the color cube tree at a particular node
             * and determines which colormap entry best represents the input
             * color.
             */
            void closestColor(int red, int green, int blue, Search search) {
                if (nchild != 0)
                    for (int id = 0; id < 8; id++)
                        if (child[id] != null)
                            child[id].closestColor(red, green, blue, search);

                if (unique != 0) {
                    int color = cube.colormap[color_number];
                    int distance = distance(color, red, green, blue);
                    if (distance < search.distance) {
                        search.distance = distance;
                        search.color_number = color_number;
                    }
                }
            }

            /**
             * Figure out the distance between this node and som color.
             */
            final static int distance(int color, int r, int g, int b) {
                return (SQUARES[((color >> 16) & 0xFF) - r + MAX_RGB]
                        + SQUARES[((color >> 8) & 0xFF) - g + MAX_RGB]
                        + SQUARES[((color >> 0) & 0xFF) - b + MAX_RGB]);
            }

            public String toString() {
                StringBuffer buf = new StringBuffer();
                if (parent == this)
                    buf.append("root");
                else
                    buf.append("node");
                buf.append(' ');
                buf.append(level);
                buf.append(" [");
                buf.append(mid_red);
                buf.append(',');
                buf.append(mid_green);
                buf.append(',');
                buf.append(mid_blue);
                buf.append(']');
                return new String(buf);
            }
        }
    }
}
